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mr Goodwill [35]
3 years ago
6

It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 househo

lds in Iowa City is taken, would you be surprised to find that fewer than 3% of households in the sample recycle their garbage? Use the fact that p-hat has an approximately normal distribution. Group of answer choices I would not be surprised because there are lots of lazy students in Iowa City. I would not be surprised because 3% is not that far away from 9%. I would be surprised because Iowa City is a very clean community which means lots of people recycle their garbage. I would be surprised because if the 9% average is true, the chance of a sample proportion being less than 3% is very small (only 1%). Who cares? It's only garbage!
Mathematics
1 answer:
BartSMP [9]3 years ago
4 0

Complete Question

It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 households in Iowa City is taken, would you be surprised to find that fewer than 3% of households in the sample recycle their garbage? Use the fact that p-hat has an approximately normal distribution.

Group of answer choices

A I would not be surprised because there are lots of lazy students in Iowa City.

B I would not be surprised because 3% is not that far away from 9%.

C I would be surprised because Iowa City is a very clean community which means lots of people recycle their garbage.

D I would be surprised because if the 9% average is true, the chance of a sample proportion being less than 3% is very small (only 1%). Who cares? It's only garbage!

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

    The sample size is  n  = 120

    The  mean of the proportion is  p =  0.09

   

Generally the standard deviation is mathematically represented as

      \sigma  =  \sqrt{\frac{p(1-p)}{n} }

=>   \sigma  =  \sqrt{\frac{0.09(1-0.09)}{120 } }

=>   \sigma  = 0.02612

Generally the chance that fewer than 3%   of households in the sample recycle their garbage is mathematically represented as

    P(X < 0.03) =  P( \frac{X - p}{\sigma}  <  \frac{0.03 -0.09}{0.02612} )

    P(X < 0.03) =  P( Z  < -2.297 )

From the z-table  

     P( Z  < -2.297 ) = 0.01

=> [tex]P(X < 0.03) = 0.01/tex]

=>   [tex]P(X < 0.03) = 1\% /tex]

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dolphi86 [110]

I'm guessing you mean

\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx

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Split up the remainder term into partial fractions. Notice that

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Then

\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52

So the integral becomes

\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}

We can simplify the result somewhat:

\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}

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3 years ago
Thank you for the help! I would appreciate it if someone could explain this content to me. I need help on both of them. I wish t
maksim [4K]
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3 years ago
Find the sum of the reciprocals of two consecutive even integers if the larger integer is x. please answer;-;​
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Step-by-step explanation:

Let the larger integer be x

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Answer:

B) no, because the corresponding angles are not congruent

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~

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